Bayesian models for prediction of the set-difference in volleyball

The aim of this paper is to study and develop Bayesian models for the analysis of volleyball match outcomes as recorded by the set-difference. Due to the peculiarity of the outcome variable (set-difference) which takes discrete values from $-3$ to $3$, we cannot consider standard models based on the usual Poisson or binomial assumptions used for other sports such as football/soccer. Hence, the first and foremost challenge was to build models appropriate for the set-differences of each volleyball match. Here we consider two major approaches: a) an ordered multinomial logistic regression model and b) a model based on a truncated version of the Skellam distribution. For the first model, we consider the set-difference as an ordinal response variable within the framework of multinomial logistic regression models. Concerning the second model, we adjust the Skellam distribution in order to account for the volleyball rules. We fit and compare both models with the same covariate structure as in Karlis & Ntzoufras (2003). Both models are fitted, illustrated and compared within Bayesian framework using data from both the regular season and the play-offs of the season 2016/17 of the Greek national men's volleyball league A1.